Math Problem Statement

Are the triangles below acute, obtuse, or right?

Solution

Let's analyze each triangle based on the angles provided to determine if they are acute, obtuse, or right triangles:

  1. Triangle A:

    • Angles: 60,30,9060^\circ, 30^\circ, 90^\circ.
    • Since there is a 9090^\circ angle, it is a right triangle.
  2. Triangle B:

    • Angles: 75,55,5075^\circ, 55^\circ, 50^\circ.
    • All angles are less than 9090^\circ, so it is an acute triangle.
  3. Triangle C:

    • Angles: 120,30,30120^\circ, 30^\circ, 30^\circ.
    • One angle is greater than 9090^\circ, making it an obtuse triangle.
  4. Triangle D:

    • Angles: 90,35,5590^\circ, 35^\circ, 55^\circ.
    • Since there is a 9090^\circ angle, it is a right triangle.

Summary of Results:

  • Triangle A - Right
  • Triangle B - Acute
  • Triangle C - Obtuse
  • Triangle D - Right

Would you like further details on any of these classifications?

Here are five related questions to deepen your understanding:

  1. What are the distinguishing properties of an acute triangle?
  2. How do we identify an obtuse triangle just by looking at its angles?
  3. Can a triangle have more than one right angle? Why or why not?
  4. How do the side lengths relate to angle types in triangles (e.g., acute, right, obtuse)?
  5. How does the Pythagorean theorem apply to right triangles?

Tip: In any triangle, the sum of the three angles will always equal 180180^\circ. This rule is helpful in verifying if the given angles form a valid triangle.

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Math Problem Analysis

Mathematical Concepts

Triangle Classification
Angles in a Triangle

Formulas

Sum of angles in a triangle = 180°

Theorems

Triangle Angle Sum Theorem

Suitable Grade Level

Grades 6-8